Abstract

Consistently with observations from recent experiments and DNS, we focus on the effects of strong velocity increments at small spatial scales for the simulation of the drag force on particles in high Reynolds number flows. In this paper, we decompose the instantaneous particle acceleration in its systematic and residual parts. The first part is given by the steady-drag force obtained from the large-scale energy-containing motions, explicitly resolved by the simulation, while the second denotes the random contribution due to small unresolved turbulent scales. This is in contrast with standard drag models in which the turbulent microstructures advected by the large-scale eddies are deemed to be filtered by the particle inertia. In our paper, the residual term is introduced as the particle acceleration conditionally averaged on the instantaneous dissipation rate along the particle path. The latter is modeled from a log-normal stochastic process with locally defined parameters obtained from the resolved field. The residual term is supplemented by an orientation model which is given by a random walk on the unit sphere. We propose specific models for particles with diameter smaller and larger size than the Kolmogorov scale. In the case of the small particles, the model is assessed by comparison with direct numerical simulation (DNS). Results showed that by introducing this modeling, the particle acceleration statistics from DNS is predicted fairly well, in contrast with the standard LES approach. For the particles bigger than the Kolmogorov scale, we propose a fluctuating particle response time, based on an eddy viscosity estimated at the particle scale. This model gives stretched tails of the particle acceleration distribution and dependence of its variance consistent with experiments.

Item Type:

Article

Additional Information:

Thanks to Amercian Physical Society editor. The original PDF of the article can be found at Amercian Physical Society website : https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.3.034602